1. Does Consulting Require Math?
Math (especially mental and business math) is essential in management consulting, due to the large amount of quantitative data involved in projects – such as in brainstorming sessions, client meetings, expert interviews, or quantitative analyses.
Management consulting is a fact-based industry – everything you say must be backed up by evidence. Most of the time, this evidence comes in the form of numbers.
This means management consultants spend a lot of their time working with numbers – during quantitative data analyses, team meetings, client interviews, etc.
2. Consulting Math vs School Math
In school, the math focuses on the numbers themselves; the context can be anything, or there can be no context at all.
With consulting math, the attention is on what those numbers mean for a business; calculations are always done in a business context, so you must be familiar with business terminology, and you do need some business intuition.
Academic math has those multivariate, exponential equations and other dreadful things haunting students’ minds throughout their school life.
Consulting math consists mostly of basic calculations. They are not necessarily easy, but at least you save some brainpower, not having to remember all those complex formulas.
In school, 100% accuracy is expected.
In consulting, meaningful insights and good decisions can be made with 90-95% accuracy, so you don’t have to be absolutely precise, especially when processing large and unrounded numbers.
The key takeaway is: your approach to consulting math should be fundamentally different from academic math. In consulting math:
- Accuracy and speed are equally important
- Small margins of error are tolerated
- All calculations are done within a business context
Comprehensive Math Drills
- 1000+ raw number calculations
- 30 chart problems
- 50 long-context and 300 short-context questions
- 10 full math cases
3. Types of Calculations in Consulting Math
Add, subtract, multiply, divide – those four basic operations form the majority of calculations done by consultants. Simple, isn’t it?
You do need to keep in mind however, that consultants usually deal with large numbers and a multitude of items in their calculations; that means you must be extra careful – forgotten zeroes aren’t good for either business or case interviews.
Equations in management consulting context are mostly used to determine the conditions required for specific outcomes (e.g.: revenue to break even).
These equations usually contain one or two variables and no power – only one step away from the most basic calculations.
Percentages are really useful to put things in perspective; effectively a fraction with a denominator of 100, percentages are often more intuitive and accurate than normal fractions (e.g.: 23% vs 3/13)
The widespread use of percentages is a distinctive feature of business language: we usually say “revenue has increased by 50%” or “we need to cut costs by 20%”; we don’t usually say 1/2 or 1/5 in those contexts.
4. Mental Math in Consulting
Why Consultants Take Mental Math So Seriously
Let’s say you are in the elevator with a client CEO, and he asks for an estimation you haven’t prepared; pulling out your smartphone to tap on the calculator app is not exactly a good way to impress your client now, is it?
In the consulting world, fast math is a must; in many situations, there is not even enough time to whip out a calculator – managers, clients and interviewers don’t want to wait; in fact, calculators are not even allowed in tests and case interviews. Quick and accurate mental math is a must-have skill.
Luckily, we have a few killer tips for you to improve your mental calculations.
How to Improve Your Mental Math – MConsultingPrep’s Secrets
For our Comprehensive Math Drills, we have developed a methodical approach to mental calculations with large numbers, consisting of two main steps: estimation & adjustment. This method is used for multiplication, division, and percentage.
- Simplify the large numbers by taking out the zeroes (e.g. 6,700,000 becomes 6.7 and 000000)
- Round the resulting 1-to-2-digit numbers for easier calculations (e.g.: 6.7 becomes 7)
- Perform simple calculations with the multiplicands
- Adjust in the opposite direction of the previous rounding and put the zeroes back in
To do percentages, multiply the original number with the numerator then divide by 100.
Let’s try a few examples, shall we?
- Take out zeroes: 12.34 x 56.78 | 00 00
- Round: 12 x 60 | 00 00
- Calculate: 720 | 0 000
- Adjust and add zeros: 7,200,000 (equal down-rounding and up-rounding roughly cancels each other out)
Accurate result: 7,006,652 | Error margin: 2.7%
- Take out zeroes: 85 / 4.5 | 00 / 0
- Round: 90 / 4.5 | 00 / 0
- Calculate: 20 | 0
- Adjust and add zeros: 190 (up-rounding means downward adjustment)
Accurate result: 189.09 | Error margin: 0.48%
- Convert %: 0.7 x 15,940
- Take out zeroes: 7 x 15.9 | One 0 in, three 0 out
- Rounding: 7 x 16 | One 0 in, three 0 out
- Calculate: 112 | One 0 in, three 0 out
- Add zeros: 11,200
- Adjust : 11,150 (up-rounding means downward adjustment)
Accurate result: 11,158 | Error margin: 0.07%
For percentage calculations, it is even easier with the “Zeros management”. We know that the final answer will have roughly the same number of digits as the original 15,940, something like 1x,xxx or x,xxx. So when having 112 after step “Calculate”, we know the final answer would be 11,2xx.
PRACTICE until this conscious process becomes part of your intuition! The harder part lies in the adjustment – the more you practice, the more accurate your adjustments will be!
To help you practice more effectively, here’s my personal tips!
Mental Math Tips:
- Write down numbers: it’s always a good idea to have visual of the number themselves on paper. This makes it 100 times easier, especially with “zeno management” work.
- Sanity check: always take a very brief moment to ask yourself “is this result logical?”; if 70% of 15,940 equals 111,500, perhaps something is wrong with your “zeros management”.
- Shortcut percentages: convert percentages into easy, common calculations (e.g.: 33%, 25%, 20% into /3, /4, /5…) if possible. In fact,kKnow as many of these shortcuts as you can.
Fast math is not enough – to pass screening test such as the PST, and to skim through piles of data in real consulting work, you’ll also need the ability to read fast!
Worry not, because there’s a scientific method that guarantees nearly instant improvement – check out this article below to find out!
5. Consulting Math Practice
To practice consulting and case interview math effectively, focus on 5 types of exercises:
- Type 1: Plain number calculations – to improve mental calculation ability
- Type 2: Short-context math – to familiarize with business-oriented math
- Type 3: Long-context math – to train on handling large amounts of context in math
- Type 4: Chart reading exercises – to improve the ability to work with chart-type data
- Type 5: Full-case math – to combine all learned techniques in a case interview setting
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5.1. Number Calculations
Numbers are at the core of every math problem, regardless of the context.
In our plain number exercises, we strip away the context so you can focus on the numbers. Absolute accuracy is not required, a margin of error less than 5% is acceptable.
We divide these exercises into eight types, which correspond with the basic calculations real consultants perform on a daily basis. Having practiced all of these calculation types, nothing will surprise you in real situations.
- Increase by Percentage
- Decrease by Percentage
- Currency Conversion – from USD
- Currency Conversion – to USD
- Time Conversion
- Big Number Comfort
5.2. Short-context Questions
Consultants are not paid to answer elementary math questions; consulting math is always put into business contexts.
These short-context questions are designed to familiarize you with such math; here, it is important to be mindful of how items relate to each other; basic knowledge of business terminology is required.
5.3. Full-context Questions
Full-context questions consist of multiple short questions, with an overarching business context.
Answering each short question requires the same knowledge and abilities as the short-context problems; however, you need to keep in mind the larger context, where key data can be found.
5.4. Chart-based Drills
Consultants love charts. Charts are very effective and efficient for visualizing data and delivering messages. If you ever wish to be a consultant, mastering the use of charts is a must.
Charts used in the consulting world can be broken down into four basic types: bar charts, line charts, pie charts, and scatter plots. Other, more complex charts are often variants or combinations of these types.
Bar charts are most effective when comparing the values of several items at one point in time, or 1-2 items at several time intervals.
However, they are unsuitable for illustrating “parts of a whole”; they also become clunky if there are too many items or time intervals (>=12).
Line charts are meant for illustrating time-series data, i.e trends in data over a continuous time period. Unlike bar charts, which use space-consuming solid bars, line charts use markers connected by straight lines to visualize data, so the number of time intervals is almost limitless.
Line charts, unfortunately, are also unsuitable for breaking down data, or visualizing more than four or five variables at a time.
Pie charts are extremely good for illustrating proportions, i.e “parts of a whole” analyses.
Nonetheless, in pie charts, all parts of the whole must be considered, and there must be no overlap (a MECE segmentation). Pie charts are also unusable for time-series data.
Scatter plots use data points to visualize how two variables relate to each other; they are capable of visualizing an infinite number of data points without compromising readability, as it is the distribution of data points that matters, not the data points themselves.
The downside of scatter plots is that the number of variables is defined and limited by the number of axes (e.g: two-axis plots illustrate two variables).
How to Read Charts Like a Real Consultant
Most people go straight for the data as soon as they come across a chart, which is opposite of what you should do. This increases the risk of misinterpreting data, leading to wrong conclusions.
Instead, follow this structured process used by real consultants in real projects, and you’ll find yourself absolutely conquering charts in no time.
Read the labels: be 120% sure what the chart is showing; look at the title, axis labels, units of measurement, categories and series, legends and footnotes to get that information.
Look for insights: how do you know what to look for in a chart? Ask yourself these questions – 1. “What is the usual purpose of this chart type?”, 2. “What’s my objective in using this chart?”, and 3. “Are there any abnormalities in the data?”.
To further demonstrate my principles, let’s take a look at this line chart:
Read the labels:
In the first few seconds, through the title, I acknowledge that the chart talks about total, global, confirmed, deaths and cases, by COVID-19; I also take into account the fact that confirmed counts are lower than actual counts.
Looking at the axes, I know that the vertical axis represents the number of cases and deaths, and the unit of measurement is million; the horizontal one illustrates a continuous time period from the start of the pandemic.
Look for insights:
What’s the purpose of this chart type? It’s a basic line chart, so I’ll initially be looking for trends in the number of confirmed COVID-19 cases and deaths. The first trend I spot in this chart is a continuous, accelerating increase.
What’s my objective? Objectives vary, depending on the context. In a test, that objective is usually defined by questions; suppose I am given the question “What’s the number of confirmed COVID-19 cases on March 21?”, I would look for that specific data point, which is around 250,000.
Is there anything abnormal? Zoom out and you’ll see a glaring abnormality on this chart – the sudden, dramatic acceleration happening around mid-March. This insight shows that a huge problem popped up immediately before March 21.
5.5. Math in Case Interview
During interviews, you not only have to solve math problems, but also draw conclusions relating to the case from the results. But what if we want to isolate the math part out and focus the practice only to that?
In our Comprehensive Math Drills, case interview math questions are shortened and modified to focus on the quantitative side.
6. Consulting Math Prep Tips
The only way to master consulting math is through constant and effective practice. Here are a few tips I used myself to ensure that I practice effectively.
- Use Your Head: Stay away from the calculator as if it’s infected with SARS-COV2. Do all your daily calculations mentally unless an EXACT answer is required.
- Flatten the Learning Curve: Doing it all in your head and still getting it right may prove challenging. At the start, a piece of scratch paper and a 5% margin of error really helps; once you are confident, discard the paper and narrow down the margin.
- Establish a Routine: Allocate some time for daily practice; this may seem hard at first, but once you’ve overcome the inertia, you can literally feel the improvement. It took me only a week of constant practice to beat my Engagement Manager, so trust me on this one.
Perfect Your Case Interview Math Skills!
Learn how to calculate like real management consultants with our Comprehensive Math Drills!
Over 1000 mental math calculations and more than 350 exercises
with detailed explanations to help you impress your case interviewer
and land an offer at top consulting firms!